by Jean Barbet | Jan 9, 2021 | Analysis, Functions, Non classé

From the complex exponential function, we can define a “circular exponential” function, which “wraps” the real line around the trigonometric circle, and makes it possible to rigorously define the cosine and sine trigonometric functions, which...
by Jean Barbet | Dec 29, 2020 | Analysis, Functions, Non classé

Some functions that can be differentiated indefinitely can be described ‘around each point’ as the sum of an power series. These are analytic functions, real or complex, the typical example being the exponential function, which can be extended to the whole complex...
by Jean Barbet | Dec 6, 2020 | Analysis, Functions

The relations between the properties of monotonicity, continuity and derivation of a function of one real variable allow us to formally derivate the inverse bijection of an injective and derivable function. The most representative example is perhaps that of the...